Areas Related To Circles

CBSE Class 10 — Maths — Previous Year Questions

Q1.VSA1 mark(2020)Easy

In Fig. 4 is a sector of circle of radius 10.5 cm. Find the perimeter of the sector. (Take $\pi =\frac{22}{7}$)

Q2.MCQ1 mark(2023)Easy

What is the length of the arc of the sector of a circle with radius $14$ cm and of central angle $90°$?
(a) $22$ cm
(b) $44$ cm
(c) $88$ cm
(d) $11$ cm

Q3.MCQ1 mark(2023)Easy

The hour-hand of a clock is 6 cm long. The angle swept by it between 7:20 a.m. and 7:55 a.m. is:
(a) $\left(\frac{35}{4}\right)°$
(b) $\left(\frac{35}{2}\right)°$
(c) $35°$
(d) $70°$

Q4.Case-Study1 mark(2023)Easy

Case Study - 1

In an annual day function of a school, the organizers wanted to give a cash prize along with a memento to their best students. Each memento is made as shown in the figure and its base ABCD is shown from the front side. The rate of silver plating is Rs. 20 per cm${}^2$.

The memento consists of a quadrant ODCO of radius 7 cm at the top and a triangle AOB with base and height of 10 cm each at the bottom.

(i) What is the area of the quadrant ODCO?

Q5.Case-Study1 mark(2023)Easy

Case Study - 1 (continued)

Refer to the memento described in Q36.

(ii) Find the area of $△AOB$.

Q6.MCQ1 mark(2023)Easy

What is the area of a semi-circle of diameter '$d$'?

Q7.Case-Study1 mark(2023)Easy

Governing council of a local public development authority of Dehradun decided to build an adventurous playground on the top of a hill, which will have adequate space for parking.

After survey, it was decided to build rectangular playground, with a semi-circular area allotted for parking at one end of the playground. The length and breadth of the rectangular playground are 14 units and 7 units, respectively. There are two quadrants of radius 2 units on one side for special seats.



Based on the above information, answer the following questions:

(i) What is the total perimeter of the parking area?

Q8.Case-Study1 mark(2023)Easy

(iii) Find the cost of fencing the playground and parking area at the rate of ₹2 per unit.

Q9.MCQ1 mark(2023)Easy

The circumferences of two circles are in the ratio $4:5$. What is the ratio of their radii?

Q10.MCQ1 mark(2024)Easy

If an arc subtends an angle of $90°$ at the centre of a circle, the ratio of its length to the circumference of the circle is:

Q11.MCQ1 mark(2024)Easy

The area of sector of a circle of radius $12$ cm is $60\pi$ cm${}^2$. The central angle of this sector is:

Q12.Assertion-Reason1 mark(2024)Easy

**Assertion (A):** If the circumference of a circle is $176$ cm, then its radius is $28$ cm.

**Reason (R):** Circumference $=2\pi \times$ radius of a circle.

Q13.MCQ1 mark(2024)Easy

The perimeter of the sector of a circle of radius 21 cm which subtends an angle of $60°$ at the centre of circle, is:

Q14.MCQ1 mark(2024)Easy

The length of an arc of a circle with radius 12 cm is $10\pi$ cm. The angle subtended by the arc at the centre of the circle, is:

Q15.MCQ1 mark(2025)Easy

If a sector of a circle has an area of $40\pi$ sq. units and a central angle of $72°$, the radius of the circle is:

Q16.MCQ1 mark(2025)Easy

A piece of wire $20$ cm long is bent into the form of an arc of a circle of radius $\frac{60}{\pi }$ cm. The angle subtended by the arc at the centre of the circle is:

Q17.Case-Study1 mark(2025)Easy

A brooch is a decorative piece often worn on clothing like jackets, blouses or dresses to add elegance. Made from precious metals and decorated with gemstones, brooches come in many shapes and designs.



One such brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure.



(i) Find the central angle of each sector.

Q18.Case-Study1 mark(2025)Easy

(ii) Find the length of the arc ACB.

Q19.MCQ1 mark(2025)Easy

If a large circular pizza is divided into 5 equal sectors, then the central angle of each sector will be:

Q20.MCQ1 mark(2025)Medium

If the area of a sector of circle of radius 36 cm is $54\pi$ cm${}^2$, then the length of the corresponding arc of the sector is:

Q21.VSA2 marks(2020)Medium

A piece of wire $22$ cm long is bent into the form of an arc of a circle subtending an angle of $60°$ at its centre. Find the radius of the circle. $\left(\text{Use }\pi =\frac{22}{7}\right)$

Q22.Case-Study2 marks(2023)Easy

Case Study - 1 (continued)

Refer to the memento described in Q36.

(iii)(a) What is the total cost of silver plating the shaded part ABCD?

Q23.Case-Study2 marks(2023)Easy

Case Study - 1 (continued)

Refer to the memento described in Q36.

(iii)(b) What is the length of arc CD?

Q24.Case-Study2 marks(2023)Medium

(ii) (a) What is the total area of parking and the two quadrants?

Q25.Case-Study2 marks(2023)Medium

(ii) (b) What is the ratio of area of playground to the area of parking area?

Q26.VSA2 marks(2024)Easy

The minute hand of a clock is $14$ cm long. Find the area on the face of the clock described by the minute hand in $5$ minutes.

Q27.VSA2 marks(2024)Easy

Find the length of the arc of a circle which subtends an angle of $60°$ at the centre of the circle of radius $42$ cm.

Q28.Case-Study2 marks(2025)Easy

(iii) (a) Find the area of each sector of the brooch.

Q29.Case-Study2 marks(2025)Easy

(iii) (b) Find the total length of the silver wire used.

Q30.VSA2 marks(2025)Medium

In the given figure, the shape of the top of a table is that of a sector of a circle with centre O and $\angle AOB=90°$. If $AO=OB=42$ cm, then find the perimeter of the top of the table.

Q31.VSA2 marks(2025)Medium

In the given figure, three sectors of a circle of radius 5 cm, making angles $35°$, $50°$ and $95°$ at the centre are shaded. Find the area of the shaded region. [Use $\pi =\frac{22}{7}$]

Q32.SA3 marks(2020)Easy

The area of a circular play ground is $22176$ cm${}^2$. Find the cost of fencing this ground at the rate of ₹$50$ per metre.

Q33.SA3 marks(2020)Medium

In Figure-8, find the area of the shaded region where a circular arc of radius 7 cm has been drawn with vertex $O$ of an equilateral triangle $OAB$ of side 14 cm as centre. (Use $\pi =\frac{22}{7}$ and $\sqrt{3}=1.73$)

Q34.SA3 marks(2020)Medium

In Figure 9, a square $OPQR$ is inscribed in a quadrant $OAQB$ of a circle. If the radius of the circle is $6\sqrt{2}$ cm, find the area of the shaded region.

Q35.SA3 marks(2023)Easy

A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle of $120°$. Find the total area cleaned at each sweep of the two blades.

Q36.SA3 marks(2023)Easy

In a circle of radius $21$ cm, an arc subtends an angle of $60°$ at the centre. Find the area of the sector formed by the arc. Also, find the length of the arc.

Q37.SA3 marks(2024)Easy

An arc of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding major sector. (Use $\pi =3.14$)

Q38.SA3 marks(2025)Medium

The length of the hour hand of a clock is 10 cm. Find the area of the minor sector swept by the hour hand of the clock between 5 a.m. to 8 a.m. Also, find the area of the major sector.

Q39.SA3 marks(2025)Medium

A chord of a circle of radius 10 cm subtends a right angle at the centre of the circle. Find the area of the corresponding minor segment. [Use $\pi =3.14$]

Q40.LA4 marks(2020)Medium

Find the area of the shaded region in Fig. 8, if $PQ=24$ cm, $PR=7$ cm and $O$ is the centre of the circle.

Q41.Case-Study4 marks(2025)Medium

The Olympic symbol comprising five interlocking rings represents the union of the five continents of the world and the meeting of athletes from all over the world at the Olympic games. In order to spread awareness about Olympic games, students of Class-X took part in various activities organised by the school. One such group of students made 5 circular rings in the school lawn with the help of ropes. Each circular ring required 44 m of rope.

Also, in the shaded regions as shown in the figure, students made rangoli showcasing various sports and games. It is given that $△OAB$ is an equilateral triangle and all unshaded regions are congruent.



Based on above information, answer the following questions:
(i) Find the radius of each circular ring.
(ii) What is the measure of $\angle AOB$?
(iii) (a) Find the area of shaded region $R_1$.

OR

(iii) (b) Find the length of rope around the unshaded regions.

Q42.LA5 marks(2023)Medium

A chord of a circle of radius 14 cm subtends an angle of $60°$ at the centre. Find the area of the corresponding minor segment of the circle. Also find the area of the major segment of the circle.

Q43.LA5 marks(2023)Medium

A horse is tied to a peg at one corner of a square shaped grass field of side $15$ m by means of a $5$ m long rope. Find the area of that part of the field in which the horse can graze. Also, find the increase in grazing area if length of rope is increased to $10$ m. (Use $\pi =3.14$)

Q44.LA5 marks(2024)Medium

An arc of a circle of radius 21 cm subtends an angle of $60°$ at the centre. Find:
(i) the length of the arc.
(ii) the area of the minor segment of the circle made by the corresponding chord.

Q45.LA5 marks(2024)Medium

The perimeter of a certain sector of a circle of radius $5.6$ m is $20.0$ m. Find the area of the sector.